Domestically, he won the 1996 Swedish league title with IFK Göteborg, ending the seasons as the league's top scorer with nineteen goals. These performances earned him moves abroad to AC Milan and Newcastle United (for whom he played in the 1998 FA Cup Final). These spells proved largely unsuccessful, resulting in Andersson's return to Sweden with AIK.

Injury problems caused him to retire on August 1, 2005, with Andersson looking to remain in football as a coach. However, he resumed playing in 2010 with Swedish minnows FC Andrea Doria.